Complex variable methods for shape sensitivity of finite element models

Shape sensitivity analysis of finite element models is useful for structural optimization and design modifications. Complex variable methods for shape sensitivity analysis have some potential advantages over other methods. In particular, for first order sensitivities using the complex Taylor series...

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Veröffentlicht in:Finite elements in analysis and design Jg. 47; H. 10; S. 1146 - 1156
Hauptverfasser: Voorhees, Andrew, Millwater, Harry, Bagley, Ronald
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Amsterdam Elsevier B.V 01.10.2011
Elsevier
Schlagworte:
Complex Taylor series expansion (CTSE)
Complex variables
Computer programs
Design sensitivities
Error detection
Exact sciences and technology
Finite differencing
Finite element method
Fourier differentiation
Fundamental areas of phenomenology (including applications)
Mathematical analysis
Mathematical models
Mathematics
Methods of scientific computing (including symbolic computation, algebraic computation)
Numerical analysis. Scientific computation
Optimization
Physics
Sciences and techniques of general use
Sensitivity analysis
Sensitivity methods
Software
Solid mechanics
Static elasticity (thermoelasticity...)
Structural and continuum mechanics
Design sensitivities
Complex Taylor series expansion (CTSE)
Fourier differentiation
Finite differencing
Sensitivity methods
Optimization
Geometrical shape
Sensitivity analysis
Displacement(deformation)
Taylor series
Modeling
Complex variable method
Finite element method
Complex method
Linear elasticity
Series expansion
Structure modification
Potential method
Differentiation
Mesh generation
Structural analysis
ISSN:0168-874X, 1872-6925
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Zusammenfassung:Shape sensitivity analysis of finite element models is useful for structural optimization and design modifications. Complex variable methods for shape sensitivity analysis have some potential advantages over other methods. In particular, for first order sensitivities using the complex Taylor series expansion method (CTSE), the implementation is straightforward, only requiring a perturbation of the finite element mesh along the imaginary axis. That is, the real valued coordinates of the mesh are unaltered and no other modifications to the software are required. Fourier differentiation (FD) provides higher order sensitivities by conducting an FFT analysis of multiple complex variable analyses around a sampling radius in the complex plane. Implementation of complex variable sensitivity methods requires complex variable finite element software such that complex nodal coordinates can be used to implement a perturbation in the shape of interest in the complex domain. All resulting finite element outputs such as displacements, strains and stresses become complex and accurate derivatives of all finite element outputs with respect to the shape parameter of interest are available. The methodologies are demonstrated using two-dimensional finite element models of linear elasticity problems with known analytical solutions. It is found that the error in the sensitivities is primarily defined by the error in the finite element solution not the error in the sensitivity method. Hence, more accurate sensitivities can be obtained through mesh refinement.
Bibliographie:ObjectType-Article-2
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content type line 23
ISSN:0168-874X
1872-6925
DOI:10.1016/j.finel.2011.05.003